The distinct element method is a numerical model capable of describing the mechanical behaviour of assemblies of discs and spheres. The method is based on the use of an explicit numerical scheme in which the interaction of the particles is monitored contact by contact and the motion of the particles modelled particle by particle. The main features of the distinct element method are described. The method is validated by comparing force vector plots obtained from the computer program BALL with the corresponding plots obtained from a photoelastic analysis. The photoelastic analysis used for the comparison is the one applied to an assembly of discs by De Josselin de Jong and Verruijt (1969). The force vector diagrams obtained numerically closely resemble those obtained photoelastically. It is concluded from this comparison that the distinct element method and the program BALL are valid tools for research into the behaviour of granular assemblies. La méthode des éléments distincts est un modèle numérique capable de décrire le comportement mécanique de l'assemblage de disques et de sphères. La méthode est basée sur l'utilisation d'un système numérique explicite dans lequel l'interaction des particules est contrôlée contact par contact et le mouvement des particules simulé particule par particule. Les caracteristiques principales de la méthode des eléments distints sont décrites. La méthode est validée en comparant les tracés de vecteur de force obtenus par le programme sur ordicateur BALL avec les tracés correspondants obtanus a l'aide d'une analyse photo-élastique. L'analyse photo-élastique utilisée pour la comparaison est celle appliquée sur un assemblage de disques par De Josselin de Jong et Verruijt (1969). Les diagrammes de vecteur de force obtenus numériquement sont très voisins de ceux obtenus photo-élastiquement. Cette comparaison permet de conclure que la methode des éléments distincts et le programme BALL sont des instruments valables pour la recherche du comportement des assemblages granulaires.

An analytic technique for solving three-dimensional interface problems in coastal aquifers is presented in this paper. Restriction is made to cases of steady state flow with homogeneous isotropic permeability where the vertical flow rates can be neglected in relation to the horizontal ones (the Dupuit-Forchheimer assumption). The aquifer is divided into zones defined by the type of flow occurring. These types of flow may be either confined, unconfined, confined interface, or unconfined interface flow, where the interfaces separate freshwater from salt water at rest. The technique is based upon the use of a single potential which is defined throughout all zones of the aquifer. This potential in each zone can be represented in a way similar to that suggested by Girinskii in 1946 and 1947. The potential introduced in this paper is single valued and continuous throughout the multiple-zone aquifer, and its application does not require that the boundaries between the zones be known in advance. The technique thus avoids the difficulties that result from the discontinuity of both the velocity gradients and the Girinskii potentials at the boundaries between the zones and from the unknown locations of these boundaries. The use of the single-valued potential is illustrated in this paper for an analytic technique, but it may be used with some advantage in numerical methods such as finite difference or finite element techniques. Applications discussed in this paper involve two interface flow problems in a shallow coastal aquifer with a fully penetrating well. The first problem is one of unconfined interface flow where the upper boundary is a free water table. The second is one of confined interface flow where the upper boundary is horizontal and impervious. Each problem involves two zones. One zone is adjacent to the coast and is bounded below by an interface between freshwater and salt water at rest. The other zone is bounded below by an impervious bottom. It is shown that saltwater intrusion in the well occurs when the discharge of the well surpasses a certain value for which the interface becomes unstable. The conditions that must be met to prevent such saltwater intrusion are established for each problem and are represented graphically.

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Groundwater mechanics is the study of fluid flow in porous media. Focusing on applications and case studies, this book explains the basic principles of groundwater flow using mathematical expressions to describe a wide range of different aquifer configurations. Emphasis is placed throughout on the importance of developing simplified models that can be solved analytically to provide insight into complex groundwater flow scenarios and to allow better interpretation of the full numerical solution. Focusing first on identifying the important features of a problem, the book explains how to translate practical questions into mathematical form and discusses the interpretation of the results. Illustrated with numerous real-world examples and graphical results, this is an ideal textbook for advanced undergraduate and graduate Earth science, geological engineering, and environmental engineering courses, as well as a useful reference for researchers and professionals.

[1] We present a review of the theory and applications of the Analytic Element Method as it exists today. The paper begins with a presentation of analytic elements used for modeling of divergence-free and irrotational flow in both two and three dimensions, including a description of the superblock approach, which makes it possible to deal effectively with very large models both in terms of accuracy and speed. We briefly discuss a particular application of the Analytic Element Method to multiaquifer problems, present the theory of the Analytic Element Method for general vector fields, and discuss the inclusion of source terms (irrotational vector fields with nonzero divergence). We finish the paper with a brief discussion of three major applications on a regional scale. INDEX